Random walk with barriers
Random walk with barriers
复制标题
有障碍的随机游走
作者：
D. Novikov;E. Fieremans;J. Jensen;J. Helpern
在多孔介质、复合材料和生物组织中，屏障（膜）对分子运动的限制无处不在。一个主要的挑战是使用批量运输测量非破坏性地表征材料或生物体的微观结构。在这里，我们演示了如何引入的渗透膜的长程结构相关性引起的运输的独特功能。我们考虑随机放置和定向的膜（d-1维平面在d维）的布朗运动的限制，并专注于使用散射方法的无序平均扩散传播。重正化群解揭示了扩散系数的标度行为的大倍，具有特征性的缓慢的反平方根时间依赖于任何d。它的起源在于空间扩展的随机限制所引入的强结构涨落，代表了结构无序的一种新的普适类。我们的结果与二维Monte Carlo模拟吻合得很好。它们可用于确定限制运输的可渗透屏障，并量化其渗透性和表面积。
Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented membranes (d − 1 dimensional planes in d dimensions) and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence for any d. Its origin lies in the strong structural fluctuations introduced by the spatially extended random restrictions, representing a novel universality class of the structural disorder. Our results agree well with Monte Carlo simulations in two dimensions. They can be used to identify permeable barriers as restrictions to transport, and to quantify their permeability and surface area.
影响因子：
4.4
作者：
Dudko, OK;Berezhkovskii, AM;Weiss, GH
通讯作者：
Weiss, GH
影响因子：
33.6
作者：
Syková E;Nicholson C
通讯作者：
Nicholson C